Unique Continuation of Weakly Conformal Mappings between Riemannian Manifolds

Conformal mappings preserving the Einstein tensor of Weyl manifolds

In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...

On a class of mappings between Riemannian manifolds

Effects of geometric constraints on a steady flow potential are described by an elliptic-hyperbolic generalization of the harmonic map equations. Sufficient conditions are given for global triviality. MSC2000 : 58E20, 58E99, 75N10.

Stability of Weakly Almost Conformal Mappings

We prove a stability of weakly almost conformal mappings in W 1,p(Ω;Rn) for p not too far below the dimension n by studying the W 1,pquasiconvex hull of the set Cn of conformal matrices. The study is based on coercivity estimates from the nonlinear Hodge decompositions and reverse Hölder inequalities from the Ekeland variational principle.

Harmonic Quasiconformal Mappings of Riemannian Manifolds

Theorems on conformal mappings of complete Riemannian manifolds and their applications

We prove several Liouville-type non-existence theorems for conformal mappings of complete Riemannian manifolds. As well, we provide applications of these results to General Relativity and to the theory of conharmonic transformations. M.S.C. 2010: 53C20.